Lecture Notes —
"Foundations of Analysis", v2.5, by J. Taylor.
Available for download at the author's website (http://www.math.utah.edu/~taylor/foundations.html).

Course Description —
We will cover chapters 7 to 10 of the notes. Main topics: Advanced
multivariable calculus. Continuity, compactness, differentiation
and affine approximation, chain rule, Taylor series, extremization,
error estimation, inverse and implicit function theorems, Riemann
integration, Fubini's Theorem, change of variables formula. The
emphasis is on further developing the student's ability to
understand more abstract concepts and to write an effective and
rigorous mathematical argument. A tentative schedule can be found
hereat http://www.math.utah.edu/~docampo/math3220/syllabus.html.

Grading —
There will be weekly homework assignments, weekly quizzes, two
in-class midterms, and a comprehensive final exam. The homework
will count for 20% of the grade, the quizzes for 20%, each of the
midterms for 15%, and the final exam for 30%. Grades will be posted
regularly on WebCT (http://webct.utah.edu).

Midterms and Final —
Exams take place in JTB 320.

First midterm

Oct. 4, 9:40am to 10:30am

Second midterm

Nov. 21, 9:40am to 10:30am

Final

Dec. 12, 8:00am to 10:00am

Quizzes —
Every Friday there will be a 10-minute quiz at the beginning of
class (except when there is a Midterm). It will contain questions
related to the material covered in class during the corresponding
week. For the quizzes, I usually give definitions a big emphasis.

Homework Assignments —
Weekly assignments and their due dates will be posted on the website.
Homework must be turned in at the beginning of class. Late homework is
not accepted.

Due Date

Assignment

Aug. 29

Section 7.1:

1, 2, 4, 5, 6, 7, 12

Section 7.2:

1, 2, 3, 4, 6, 9, 12, 13

Sept. 6

Section 7.3:

1, 2, 3, 4, 5, 6, 7, 8

9, 10, 11, 14, 15

Sept. 13

Section 7.4:

2, 4, 5, 7, 8, 9, 10, 12

13, 15

Sept. 20

Section 7.5:

1, 2, 4, 5, 7, 8, 9

10, 14

Sept. 27

Section 8.1:

1, 3, 5, 9

Section 8.2:

1, 3, 5, 6, 8

Oct. 5

Section 8.3:

1, 2, 3, 4, 5, 7, 8

Oct. 18

Section 8.4:

1, 2, 3, 5, 7, 8, 9, 10

14, 15

Section 8.5:

1, 2, 3, 5, 7, 8, 9, 10

Nov. 2

Section 9.1:

2, 4, 6, 8, 10

Section 9.2:

1, 2, 3, 4, 6, 9, 10, 12

Section 9.3:

2, 3, 5, 8

Nov. 9

Section 9.3:

9, 10, 11

Section 9.4:

1, 2, 3, 4, 8, 11, 12

13, 14

Nov. 21

Section 9.5:

1, 2, 5, 6, 7, 8

Section 9.6:

1, 2, 3, 4, 5, 10

Section 9.7:

1, 2, 4, 6, 7

Nov. 30

Section 10.1:

1, 3, 4, 5, 6, 10

Section 10.2:

2, 4, 6, 7

ADA Statement —
The Americans with Disabilities Act requires that reasonable
accommodations be provided for students with physical, cognitive,
systemic, learning, and physical disabilities. Please contact me at
the beginning of the semester to discuss any such accommodations
you may require for this course.